Question: Michael is 5 times as old as Omar. Four years ago, Michael was 7 times as old as Omar. How old is Michael now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and Omar. Let Michael's current age be $m$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $m = 5o$ Four years ago, Michael was $m - 4$ years old, and Omar was $o - 4$ years old. The information in the second sentence can be expressed in the following equation: $m - 4 = 7(o - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = m / 5$ . Substituting this into our second equation, we get: $m - 4 = 7($ $(m / 5)$ $- 4)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 4 = \dfrac{7}{5} m - 28$ Solving for $m$ , we get: $\dfrac{2}{5} m = 24$ $m = \dfrac{5}{2} \cdot 24 = 60$.